A transit survey monitors Sun-like stars ( ) and finds planets on circular orbits of…

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Astrophysics & Cosmology · Celestial mechanics and planetary systems

Stars from the Inside, Ch Planetary systems: formation estimates, transits and the atmospheres of other worlds

Problem

A transit survey monitors N∗=8000N_* = 8000 Sun-like stars (R∗=R⊙R_* = R_\odot) and finds 55 planets on circular orbits of semi-major axis a=0.5 AUa = 0.5\,\mathrm{AU}, all detected with pipeline completeness η=0.60\eta = 0.60. Each planet's geometric transit probability is ptr=R∗/ap_{\rm tr} = R_*/a. Using f=N∗−1∑j(ptr,j ηj)−1,f = N_*^{-1}\sum_j (p_{{\rm tr},j}\,\eta_j)^{-1}, estimate the occurrence rate ff of such planets per star.

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